1. Field of the Invention
The invention relates in general to protective relay apparatus for electrical power systems, and more specifically to impedance distance relays for the protection of electrical power transmission lines.
2. Description of the Prior Art
Protective relaying apparatus for ac electrical power systems must discriminate between faults and normal system transients, and it must make a trip/no-trip decision quickly in order to maintain system stability, minimize fault current damage, and maintain system security. One class of protective relaying apparatus for transmission line protection is the impedance distance relay. The impedance distance relay measures the impedance of the transmission line from the location of the relay to the fault location, and if the fault lies within the protection zone of an associated circuit breaker, the circuit breaker is immediately tripped. If the fault is outside the protection zone, the circuit breaker is not immediately tripped. It may, however, be tripped after a suitable time delay, selected to allow the tripping of other breakers, in order to provide coordinated back-up protection for adjacent breakers.
In an electromechanical distance relay, the hardware completely defines the operating characteristics, with the induction cylinder providing the multiplying/integrating functions which generate the required protection zone on the R/X plane.
It would seem that the digital computer could be programmed to provide the functions of an ideal distance relay, because of its operating speed, the ability to provide almost any desired protection zone geometry, and the fact that it may perform many complex calculations per cycle of the system power frequency. Mathematical formulas, which require as few as three samples to predict the peak of a current sinusoid make the use of a digital computer even more attractive, as the sampling of the voltage and current waveforms need not be synchronized to the phase position of the alternating parameter being measured. For example, a sample of data, and its derivative, may be used; or, as disclosed in U.S. Pat. No. 3,731,152, which is assigned to the same assignee as the present application, the peak magnitude of a sinusoidal quantity may be determined by using the first and second derivatives of the quantity. As hereinbefore stated, three consecutive samples are required to make the calculation, and thus the algorithm has an aperture or data window of three samples. In other words, a time length of twice the sample spacing. In order to correctly predict fault current magnitude, the three consecutive samples must follow the fault inception point, as pre-fault values in the data window would naturally give an incorrect prediction of peak magnitude.
Thus, it would appear that a digital computer could be easily programmed to detect a fault, make three impedance calculations of three digitized successive samples following fault inception, and correctly make a trip/no-trip decision. This will be true if the fault waveforms are pure sinusoids. In practice, however, the fault waveforms are usually distorted. For example, the current waveform may have a dc offset transient, the magnitude of which may be as large as the fault current peak. The magnitude depends upon a variety of factors, such as the fault inception angle and pre-fault load current. Line reactance prevents an instantaneous change in current from load to fault value, creating this decaying exponential dc transient as the system changes from a pre-fault steady state condition, to a post-fault steady state condition. The voltage and current waveforms are not immune to other distortion either, as they may contain harmonics, transients, and other high frequency noise, such as caused by non-linear elements, surge reflections, current transformer saturation, and the like.
Thus, it will easily be seen that an algorithm which makes its decision after three data samples can make an incorrect prediction of peak magnitude, if the waveforms are distorted.
The hereinbefore mentioned algorithm of U.S. Pat. No. 3,731,152, which uses first and second differentials or differences instead of the sample and the first differential or difference, reduces the sensitivity of the algorithm to frequencies below power frequency, including the dc offset, but it is extremely sensitive to higher frequencies because of the additional differentiation. Thus, some sort of post-algorithm averaging or integration must be used to stabilize the output signals and provide data from which intelligent trip/no-trip decisions may be made.
The samples may of course be digitally filtered by a suitable filtering program, prior to applying the samples to the algorithm step, but many more samples must be taken before a post-fault steady state calculation may be reached, extending the data window and thus the time following fault inception before an accurate trip/no-trip decision may be made. Also, digital filtering programs may require more computation time than possible with a microprocessor, especially with a high sampling rate. It would be desirable to provide a program implementable with a microprocessor, because of the attractive economic factors associated with microprocessors. The results of the algorithm may also be processed, such as by numerical integration, to preclude noise induced trips, but again extending the data window.
Instead of attempting to expand a three sample data window algorithm by some sort of pre- and/or post-algorithm processing, other algorithms have been developed which inherently perform substantial filtering of the data. For example, Fourier and Walsh type algorithms have been developed in which the data is filtered in the algorithm itself. These algorithms provide band pass characteristics central about power frequency, and provide a steady state, accurate impedance calculation one full cycle of samples following fault inception, and thus these algorithms have a data window equal to one full power frequency cycle. Thus, the present practice is to pick an algorithm, deemed to be the best compromise between security and speed, for the specific transmission line to be protected.